Group #36353421 — subgroups

Subgroups — #36353421

Order 22144.

260 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19149608	C₂	1	2	yes	maximal
2	C₂×#19149590	C₂	1	1	yes	maximal, characteristic
3	#26011337	C₂	1	1	yes	maximal, characteristic
4	#26011245	C₂	1	2	yes	maximal
5	C₂×C₄×C₈×C₁₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#13063436	C₂²	1	2	yes	—
7	C₂×C₄×Dic₁₇₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₁₇₃	C₂²	1	1	yes	characteristic
9	#19149608	C₄	1	8	yes	complemented
10	#19149590	—	2	2	no	—
11	#19149586	C₄	1	4	yes	—
12	C₂²×C₈×C₁₇₃	C₂²	1	2	yes	—
13	C₂×C₄²×C₁₇₃	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₁₇₃	—	2	2	no	—
15	C₂²×Dic₁₇₃	C₂×C₄	1	2	yes	—
16	C₂²×Dic₁₇₃	C₂×C₄	1	2	yes	—
17	C₂×#13063436	—	2	2	no	—
18	C₂×#13063436	—	2	2	no	—
19	C₂×#13063436	C₂×C₄	1	4	yes	—
20	C₄×Dic₁₇₃	—	2	2	no	—
21	C₄×Dic₁₇₃	C₂×C₄	1	4	yes	—
22	C₂²×C₄×C₁₇₃	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
24	C₂×C₈×C₁₇₃	—	2	2	no	—
25	C₂×C₈×C₁₇₃	—	2	2	no	—
26	C₂×C₈×C₁₇₃	C₂×C₄	1	4	yes	—
27	C₄²×C₁₇₃	D₄	1	2	yes	—
28	C₄²×C₁₇₃	Q₈	1	2	yes	—
29	C₂×Dic₁₇₃	—	2	4	no	—
30	C₂×Dic₁₇₃	—	2	2	no	—
31	C₂×Dic₁₇₃	—	2	4	no	—
32	C₂×Dic₁₇₃	C₄²	1	4	yes	—
33	#13063436	—	2	4	no	—
34	C₂³×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₇₃	—	2	4	no	—
36	C₂×C₄×C₁₇₃	C₄⋊C₄	1	4	yes	—
37	C₂×C₄×C₁₇₃	C₂²×C₄	1	2	yes	—
38	C₂×C₄×C₁₇₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₇₃	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₁₇₃	#41	1	2	yes	—
41	C₈×C₁₇₃	—	2	4	no	—
42	C₂²×C₁₇₃	C₂×C₄²	1	1	yes	characteristic
43	C₂²×C₁₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂²×C₁₇₃	#117	1	1	yes	characteristic
45	C₂²×C₁₇₃	#131	1	4	yes	—
46	C₄×C₁₇₃	—	2	4	no	—
47	C₄×C₁₇₃	C₄×D₄	1	2	yes	—
48	C₄×C₁₇₃	C₄×Q₈	1	2	yes	—
49	Dic₁₇₃	—	2	4	no	—
50	Dic₁₇₃	—	4	2	no	—
51	C₂×C₁₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₁₇₃	#405	1	2	yes	—
53	C₂×C₁₇₃	#424	1	2	yes	—
54	C₂×C₁₇₃	#433	1	2	yes	—
55	C₁₇₃	#1768	1	1	yes	characteristic, complemented, Sylow
56	#1768	—	173	1	no	maximal, Sylow
57	C₂×C₄⋊C₈	—	173	2	no	—
58	C₂×#97	—	173	1	no	—
59	C₂×C₄×C₈	D₁₇₃	1	1	yes	characteristic
60	#376	—	173	1	no	—
61	#336	—	173	2	no	—
62	C₂²×C₈	—	173	2	no	—
63	C₂²×C₈	C₂×D₁₇₃	1	2	yes	—
64	C₂×C₄²	—	173	1	no	—
65	C₂×C₄²	—	173	1	no	—
66	C₂×C₄²	C₂×D₁₇₃	1	1	yes	characteristic
67	C₄⋊C₈	—	173	8	no	—
68	#97	—	346	2	no	—
69	C₄×C₈	—	2	2	no	—
70	#95	—	173	4	no	—
71	C₂²×C₄	—	173	2	no	—
72	C₂²×C₄	—	173	2	no	—
73	C₂²×C₄	C₄×D₁₇₃	1	2	yes	—
74	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	—	2	2	no	—
77	C₂×C₈	—	346	2	no	—
78	C₂×C₈	—	346	2	no	—
79	C₂×C₈	—	173	4	no	—
80	C₂×C₈	C₄×D₁₇₃	1	4	yes	—
81	C₄²	—	346	2	no	—
82	C₄²	—	173	4	no	—
83	C₄²	C₂²⋊D₁₇₃	1	2	yes	—
84	C₄²	Dic₃₄₆	1	2	yes	—
85	C₂³	C₂×C₄×D₁₇₃	1	1	yes	characteristic
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	346	4	no	—
88	C₂×C₄	—	346	2	no	—
89	C₂×C₄	—	346	4	no	—
90	C₂×C₄	—	173	4	no	—
91	C₂×C₄	#14583805	1	4	yes	—
92	C₂×C₄	C₂×C₄×D₁₇₃	1	2	yes	—
93	C₂×C₄	C₂×C₂²⋊D₁₇₃	1	1	yes	characteristic
94	C₂×C₄	C₂×Dic₃₄₆	1	1	yes	characteristic
95	C₂×C₄	#14583826	1	2	yes	—
96	C₈	—	2	4	no	—
97	C₈	—	346	4	no	—
98	C₂²	C₄²×D₁₇₃	1	1	yes	characteristic
99	C₂²	C₂×#14583805	1	1	yes	characteristic
100	C₂²	#19149636	1	1	yes	characteristic
101	C₂²	#19149685	1	4	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	346	4	no	—
104	C₄	—	692	2	no	—
105	C₄	C₄×C₂²⋊D₁₇₃	1	2	yes	—
106	C₄	C₄×Dic₃₄₆	1	2	yes	—
107	C₂	C₄×#14583805	1	1	yes	characteristic
108	C₂	#26011445	1	2	yes	—
109	C₂	#26011517	1	2	yes	—
110	C₂	#26011550	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19149608

C₂

yes

maximal

C₂×#19149590

C₂

yes

maximal, characteristic

#26011337

C₂

yes

maximal, characteristic

#26011245

C₂

yes

maximal

C₂×C₄×C₈×C₁₇₃

C₂

yes

maximal, characteristic

C₂²×#13063436

C₂²

yes

—

C₂×C₄×Dic₁₇₃

C₂²

yes

characteristic

C₂×C₄×Dic₁₇₃

C₂²

yes

characteristic

#19149608

C₄

yes

complemented

#19149590

—

#19149586

C₄

yes

—

C₂²×C₈×C₁₇₃

C₂²

yes

—

C₂×C₄²×C₁₇₃

C₂²

yes

characteristic

C₄×C₈×C₁₇₃

—

C₂²×Dic₁₇₃

C₂×C₄

yes

—

C₂²×Dic₁₇₃

C₂×C₄

yes

—

C₂×#13063436

—

C₂×#13063436

—

C₂×#13063436

C₂×C₄

yes

—

C₄×Dic₁₇₃

—

C₄×Dic₁₇₃

C₂×C₄

yes

—

C₂²×C₄×C₁₇₃

C₂×C₄

yes

—

C₂²×C₄×C₁₇₃

C₂³

yes

characteristic

C₂×C₈×C₁₇₃

—

C₂×C₈×C₁₇₃

—

C₂×C₈×C₁₇₃

C₂×C₄

yes

—

C₄²×C₁₇₃

D₄

yes

—

C₄²×C₁₇₃

Q₈

yes

—

C₂×Dic₁₇₃

—

C₂×Dic₁₇₃

—

C₂×Dic₁₇₃

—

C₂×Dic₁₇₃

C₄²

yes

—

#13063436

—

C₂³×C₁₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₇₃

—

C₂×C₄×C₁₇₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₇₃

C₂²×C₄

yes

—

C₂×C₄×C₁₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₇₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₇₃

#41

yes

—

C₈×C₁₇₃

—

C₂²×C₁₇₃

C₂×C₄²

yes

characteristic

C₂²×C₁₇₃

C₂×C₄⋊C₄

yes

C₂²×C₁₇₃

yes

C₂²×C₁₇₃

yes

—

C₄×C₁₇₃

—

C₄×C₁₇₃

C₄×D₄

yes

—

C₄×C₁₇₃

C₄×Q₈

yes

—

Dic₁₇₃

—

Dic₁₇₃

—

C₂×C₁₇₃

C₄×C₄⋊C₄

yes

characteristic

C₂×C₁₇₃

#405

yes

—

C₂×C₁₇₃

#424

yes

—

C₂×C₁₇₃

#433

yes

—

C₁₇₃

#1768

yes

characteristic, complemented, Sylow

#1768

—

173

maximal, Sylow

C₂×C₄⋊C₈

—

173

—

C₂×#97

—

173

—

C₂×C₄×C₈

D₁₇₃

yes

characteristic

#376

—

173

—

#336

—

173

—

C₂²×C₈

—

173

—

C₂²×C₈

C₂×D₁₇₃

yes

—

C₂×C₄²

—

173

—

C₂×C₄²

—

173

—

C₂×C₄²

C₂×D₁₇₃

yes

characteristic

C₄⋊C₈

—

173

—

#97

—

346

—

C₄×C₈

—

#95

—

173

—

C₂²×C₄

—

173

—

C₂²×C₄

—

173

—

C₂²×C₄

C₄×D₁₇₃

yes

—

C₂²×C₄

C₂²×D₁₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

346

—

C₂×C₈

—

346

—

C₂×C₈

—

173

—

C₂×C₈

C₄×D₁₇₃

yes

—

C₄²

—

346

—

C₄²

—

173

—

C₄²

C₂²⋊D₁₇₃

yes

—

C₄²

Dic₃₄₆

yes

—

C₂³

C₂×C₄×D₁₇₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

346

—

C₂×C₄

—

346

—

C₂×C₄

—

346

—

C₂×C₄

—

173

—

C₂×C₄

#14583805

yes

—

C₂×C₄

C₂×C₄×D₁₇₃

yes

—

C₂×C₄

C₂×C₂²⋊D₁₇₃

yes

characteristic

C₂×C₄

C₂×Dic₃₄₆

yes

characteristic

C₂×C₄

#14583826

yes

—

C₈

—

C₈

—

346

—

C₂²

C₄²×D₁₇₃

yes

characteristic

C₂²

C₂×#14583805

yes

characteristic

100

C₂²

#19149636

yes

characteristic

101

C₂²

#19149685

yes

—

102

C₄

—

103

C₄

—

346

—

104

C₄

—

692

—

105

C₄

C₄×C₂²⋊D₁₇₃

yes

—

106

C₄

C₄×Dic₃₄₆

yes

—

107

C₂

C₄×#14583805

yes

characteristic

108

C₂

#26011445

yes

—

109

C₂

#26011517

yes

—

110

C₂

#26011550

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₇₃
commutator	C₂²×C₁₇₃	C₂×C₄²
Fitting	C₂×C₄×C₈×C₁₇₃	C₂
socle, prime radical	C₂³×C₁₇₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₇₃	C₂³
hypercenter	C₂×C₄×C₈	D₁₇₃
hypocenter	C₁₇₃	#1768
LCS	G ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₇₃

commutator

C₂²×C₁₇₃

C₂×C₄²

Fitting

C₂×C₄×C₈×C₁₇₃

C₂

socle, prime radical

C₂³×C₁₇₃

C₂²×C₄

cosocle

C₂²×C₄×C₁₇₃

C₂³

hypercenter

C₂×C₄×C₈

D₁₇₃

C₁₇₃

G ▷ C₂²×C₁₇₃ ▷ C₁₇₃

C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
9. #19149608	C₄	semidirect
55. C₁₇₃	#1768	semidirect

H ≅ G/N

type

9. #19149608

C₄

semidirect

55. C₁₇₃

#1768

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#19149608	2
C₂×#19149590	2
#26011337	2
#26011245	2
C₂×C₄×C₈×C₁₇₃	2
#1768	173

subgroup

index

C₂×C₄×C₈×C₁₇₃

173

Subgroups — #36353421

Conjugacy classes of subgroups

Complements

Maximal subgroups